Batman: "A hero can be anyone. Even a man doing something as simple and reassuring as putting a coat around a little boy's shoulder to let him know that the world hadn't ended."

THE BOMB IS TRIGGERED !!, IT WOULD BLOW UP IN A FEW MINUTES !!

BATMAN resorts to his BAT and decides to head towards the ocean with the bomb.

However in front of him lies a huge grid of tall buildings. Starting from the top-leftmost grid he needs to move to the bottom right-most grid to reach the ocean. Since the fuel of BAT has nearly exhausted, BATMAN decides to chose a path where the maximum up distance travelled at a time is minimized. However, each movement of the BAT up or down the building takes one unit of time. (Horizontal movements can be made in no time). The clock keeps ticking, So BATMAN decides to choose a path reaching the destination minimizing the maximum up distance and with as much time left as possible.

Every Hero Has a Journey. Every Journey Has an End !

CatWoman : "You don't owe these people anymore. You've given them everything."
BatMan : "Not everything, not yet."

NOTES :

• BatMan requires to take the first jump on (1, 1)
• Print NO is no time is left.
• Minimum max up-distance is the first priority.

Input

The first line contains T, the number of test cases.

In each test case, the first line contains N (the size of the grid) and M (the time left).

The next N lines contain N integers, denoting the heights of the building.

Output

If BATMAN could reach the destination, print "YES", the maximum up distance travelled and the maximum time left with BATMAN.

If he could not reach the destination within time, print "NO".

Constraints

1 ≤ N ≤ 20

1 ≤ M ≤ 100

Example

Input:
1
3 40
2 4 3
4 5 3
2 4 6

Output:
YES : 2 32